This document summarizes the Apex pension models developed by the World Bank to compare pension systems across countries. It describes the methodology, assumptions, inputs, and key outputs of the models. The models calculate pension entitlements for hypothetical new pensioners based on each country's pension rules. The key outputs include gross and net pension levels, replacement rates, and pension wealth. Examples are provided comparing outputs for different pension formulas and countries.

1. Measuring Pension
Entitlements II
Sergi Biletsky
HDNSP, World Bank
April 4, 2013

2. APEX Pension Models
 Apex (Analysis of Pension Entitlements across Countries)
is a collection of country pension and tax models based on
a single set of economic assumptions to ensure
comparability across countries
 Apex includes user interface employing customized
STATA dialogues, and STATA routines describing each
country pension, personal tax and social contribution
systems and calculation procedures
 Originally developed by Edward Whitehouse and used by
the World Bank, OECD, and European Commission

3. Methodology and Assumptions(1)
 All calculations are done for new pensioners only and
based on national pension and tax system parameters
and rules at the year of modeling, including legislated
reforms that are being phased in
 Pension entitlements are computed for individuals
entering employment in that year, and as if they had
worked their entire career under currently legislated
pension and tax regimes

4. Methodology and Assumptions(2)
 The results are produced for different levels of earnings
and years of service (earnings are conveniently presented
as a fraction or multiple of the economy-wide average
wage)
 Uniform economic assumptions: inflation (p=2.5%), real
earnings growth (w=2%), real rate of return (r=3.5%), real
discount rate (z=2%), and mortality rates (m) from the
UN Population Database

5. Key Inputs
Benefit levels …as a function of system
parameters and economic
variables
Defined Benefit Pension = Accrual Rate * Years of Service * Reference
Wage
Defined Contribution Pension = Account Balance / Annuity Factor
Account Balance = C1*(1+r)N + C2*(1+r)N-1
+…+ CN*(1+r),
where Ct = Contribution Ratet * Waget
and N are years of service.
Annuity Factor is a function of mortality rates
(m), indexation to wage growth (w) and/or
inflation (p), and a discount rate (z)

6. Key Outputs (1)
 Gross Pension Level = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝐺𝑟𝑜𝑠𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑒𝑐𝑜𝑛𝑜𝑚𝑦 𝑤𝑖𝑑𝑒 𝑤𝑎𝑔𝑒
 Gross RR = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝐺𝑟𝑜𝑠𝑠 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑤𝑎𝑔𝑒
 Gross Pension Wealth = Gross Pension Level * 𝐴𝐹𝑟𝑒𝑡.𝑎𝑔𝑒

7. Examples
 Flat rate pension scheme
0
0.5
1
1.5
2
2.5
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Grossrelativepensionlevel
Individual earnings, proportion of average earnings
Social
0
0.25
0.5
0.75
1
1.25
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Grossreplacementrate
Individual earnings, proportion of average earnings
Social
Individual earnings, multiple of average
0.5 0.75 1.0 1.5 2.0
Gross pension level
(% of average earnings)
40.0 40.0 40.0 40.0 40.0
Gross replacement rate
(% of individual earnings)
80.0 53.3 40.0 26.7 20.0
Gross pension wealth, male
(multiple of average earnings) 7.2 7.2 7.2 7.2 7.2

8. Examples
 Combination of flat rate and earnings related (DC) schemes
0
0.5
1
1.5
2
2.5
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Grossrelativepensionlevel
Individual earnings, proportion of average earnings
Social Contributory
0
0.25
0.5
0.75
1
1.25
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Grossreplacementrate
Individual earnings, proportion of average earnings
Social Contributory
Individual earnings, multiple of average
0.5 0.75 1.0 1.5 2.0
Gross pension level
(% of average earnings)
24.8 32.5 40.3 55.8 71.3
Gross replacement rate
(% of individual earnings)
49.6 43.4 40.3 37.2 35.6
Gross pension wealth, male
(multiple of average earnings) 3.42 4.49 5.56 7.70 9.84

9. Examples
 Two-tier pension system in Bulgaria
Individual earnings, multiple of average
0.5 0.75 1.0 1.5 2.0
Gross pension level
(% of average earnings)
37.6 56.3 75.1 106.0 116.5
Gross replacement rate
(% of individual earnings)
75.1 75.1 75.1 70.6 58.3
Gross pension wealth, male
(multiple of average earnings) 11.2 11.2 11.2 10.5 8.6
0
.25
.5
.75
1
1.25
Grossreplacementrate
0 .25 .5 .75 1 1.25 1.5 1.75 2
Individual earnings, proportion of average earnings
DC Earnings-related
0
.5
1
1.5
2
2.5
0 .25 .5 .75 1 1.25 1.5 1.75 2
Individual earnings, proportion of average earnings
DC Earnings-related

10. Key Outputs (2)
 Gross Pension Level = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝐺𝑟𝑜𝑠𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑒𝑐𝑜𝑛𝑜𝑚𝑦 𝑤𝑖𝑑𝑒 𝑤𝑎𝑔𝑒
 Gross RR = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝐺𝑟𝑜𝑠𝑠 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑤𝑎𝑔𝑒
 Gross Pension Wealth = Gross Pension Level * 𝐴𝐹𝑟𝑒𝑡.𝑎𝑔𝑒
 Net RR = 𝑁𝑒𝑡 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝑁𝑒𝑡 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑤𝑎𝑔𝑒
 Net Pension Wealth = Net Pension Level * 𝐴𝐹𝑟𝑒𝑡.𝑎𝑔𝑒

11. Examples
 Two-tier pension system in Bulgaria
Individual earnings, multiple of average
0.5 0.75 1.0 1.5 2.0
Net replacement rate
(% of individual earnings)
95.0 95.0 95.0 89.3 73.6
Net pension wealth, male
(multiple of average earnings) 11.2 11.2 11.2 10.5 8.6
Average tax rate: worker
(% of individual earnings)
20.9 20.9 20.9 20.9 20.9
Average tax rate: pensioner
(% of individual earnings)
0.0 0.0 0.0 0.0 0.0
0
.25
.5
.75
1
1.25
0 .25 .5 .75 1 1.25 1.5 1.75 2
Individual earnings, proportion of average earnings
Net Gross

12. Key Outputs (3)
 Gross Pension Level = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝐺𝑟𝑜𝑠𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑒𝑐𝑜𝑛𝑜𝑚𝑦 𝑤𝑖𝑑𝑒 𝑤𝑎𝑔𝑒
 Gross RR = 𝐺𝑟𝑜𝑠𝑠 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝐺𝑟𝑜𝑠𝑠 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑤𝑎𝑔𝑒
 Gross Pension Wealth = Gross Pension Level * 𝐴𝐹𝑟𝑒𝑡.𝑎𝑔𝑒
 Net RR = 𝑁𝑒𝑡 𝑃𝑒𝑛𝑠𝑖𝑜𝑛
𝑁𝑒𝑡 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑤𝑎𝑔𝑒
 Net Pension Wealth = Net Pension Level * 𝐴𝐹𝑟𝑒𝑡.𝑎𝑔𝑒
 Progressivity Index = 1 - 𝑃𝑒𝑛𝑠𝑖𝑜𝑛 𝐺𝑖𝑛𝑖
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐺𝑖𝑛𝑖

13.  Gini = A/(A+B)

14. Examples
 Redistribution in Belarus
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
Grossrelativepensionlevel
Individual earnings, proportion of average earnings
Gross pension level - PAYG
Gross pension level - NDC (in 2045)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9
Grossreplacementrate
Individual earnings, proportion of average earnings
Gross pension level - PAYG
Gross replacement rate - NDC (in 2045)
Individual earnings, multiple of average
0.5 0.75 1.0 1.5 2.0
Gross pension level
(% of average earnings)
29.8 36.3 42.3 46.8 50
Gross replacement rate
(% of individual earnings)
59.6 48.4 42.3 31.2 25
Gross pension wealth
(multiple of average earnings)
5.3 (Male) 6.4 (Male) 7.4 (Male) 8.2 (Male) 8.8 (Male)
8.1 (Female) 9.8 (Female) 11.4 (Female) 12.6 (Female) 13.5 (Female)

15. Examples
 Progressivity of pension formulae
Pension Gini Progressivity index Gini wage
Sweden 26.4 -14.4 23.1
Hungary 33.6 0 33.6
Italy 23.3 1.8 23.7
Poland 29.2 4.1 30.5
Netherlands 24.3 5.7 25.7
Finland 22.6 5.9 24
Spain 25.7 17.1 31.1
Germany 19.8 24.7 26.3
Norway 13.6 38.1 22
Japan 14.3 46 26.4
United States 16.1 50.8 32.7
Belgium 10.2 52.6 21.6
Czech Republic 8.8 65.5 25.5
Korea 10.2 65.5 29.6
Belarus 11.2 67.5 34.5
Australia 8.1 70.1 27.2
United Kingdom 5.1 82.4 28.9
Ireland 0 100 29.6
New Zealand 0 100 27.7
OECD 18 16.2 39.8 27.2

16. Thank You!